ARTICLE IN PRESS. The Spanish Review of Financial Economics xxx (2012) xxx xxx. The Spanish Review of Financial Economics.

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1 The Spanish Review of Financial Economics xxx (2012) xxx xxx The Spanish Review of Financial Economics Article From PIN to VPIN: An introduction to order flow toxicity David Abad a,, José Yagüe b a Universidad de Alicante, Dpto. Economía Financiera y Contabilidad, Facultad de Ciencias Económicas y Empresariales, Ctra. San Vicente, s/n, San Vicente del Raspeig (Alicante), Spain b Universidad de Murcia, Dpto. Organización de Empresas y Finanzas, Facultad de Economía y Empresa, Campus de Espinardo, s/n, Murcia, Spain a r t i c l e i n f o Article history: Received 9 August 2012 Accepted 30 October 2012 Available online xxx JEL classification: G12 G14 C58 D53 Keywords: PIN VPIN Order flow toxicity High frequency trading (HFT) Adverse selection Probability of informed trading Market microstructure a b s t r a c t As an update of the well-known PIN measure, Easley et al. (2012a) have developed a new measure of order flow toxicity called Volume-Synchronized Probability of Informed Trading or VPIN. Order flow toxicity makes reference to adverse selection risk but applied to the world of high frequency trading (HFT). We provide a detailed description of the VPIN estimation procedure paying special attention to the main innovations introduced and the key variables of this novel tool. By using a sample of stocks listed on the Spanish market, we compare VPIN to PIN. Although VPIN metric is conceived for the HFT environment, our results suggest that certain VPIN specifications provide proxies for adverse selection risk similar to those obtained by the PIN model. Thus, we consider that the key variable in the VPIN procedure is the number of buckets used and that VPIN can be a helpful device which is not exclusively applicable to the HFT world Asociación Española de Finanzas. Published by Elsevier España, S.L. All rights reserved. 1. Introduction The 2010 Flash Crash is without a doubt the shortest event in the recent history of financial markets to merit so much attention and generate so much controversy among practitioners and academics. On May 6th 2010 the Dow Jones Industrial Average plunged about 1000 points or about 9% only to recover those losses within minutes. 1 Although the ultimate cause of the Flash Crash is still under discussion (e.g., Kirilenko et al., 2011; Madhavan, 2012) This paper is inspired by the comments that David Abad made about a preliminary version of Easley et al. (2012a) presented at the Workshop High Frequency Trading: Financial and Regulatory Implications held in Madrid, October David Abad appreciates helpful comments from Maureen O Hara and Marcos López de Padro. David Abad acknowledges financial support from the Ministerio de Ciencia e Innovación through grants ECO and ECO José Yagüe acknowledges financial support from Fundación Caja Murcia. The authors also thank Roberto Pascual for his constructive comments, as well as Zheng Junyan for the help in programming of PIN estimation. Corresponding author. addresses: goliat@ua.es (D. Abad), ppyague@um.es (J. Yagüe). 1 The 2010 Flash Crash is also known as The Crash of 2:45 or just simply, the Flash Crash. it is generally accepted that this event was the result of a new trading paradigm emanating from legislative changes in the US ( Regulation National Market System of 2005, or Reg NMS ) and Europe ( Markets in Financial Instruments Directive of 2007, or MiFID ) and prompted by substantial technological advances in computation and communication. The new legislative environment fostered both greater competition and market fragmentation while technological advances made high-speed trading technically possible at and between different trading venues. As a result, the world of high frequency trading (HFT) has appeared as a new reality in current markets that is progressively outshining traditional or low frequency trading (LFT). 2 A number of studies indicate that HFT is playing a crucial role in liquidity supply activity in current markets. Hasbrouck and Saar (2012), by analyzing low-latency activity (i.e., trading strategies that respond to market events in the millisecond environment) find that it improves traditional market quality measures such as the liquidity in the limit order book. Similarly, Brogaard et al. (2012) 2 Easley et al. (2012c) provide a detailed description of this new paradigm and how HFT exploits LFT s structural weaknesses /$ see front matter 2012 Asociación Española de Finanzas. Published by Elsevier España, S.L. All rights reserved.

2 2 D. Abad, J. Yagüe / The Spanish Review of Financial Economics xxx (2012) xxx xxx find evidence of HFT benefitting price efficiency and the provision of liquidity at stressful times such as the most volatile days and before and after macroeconomic news announcements. Nevertheless, in the HFT environment the liquidity provision activity and its associated risks acquire a new dimension. Thus, Easley et al. (2012a) introduce the concept of order flow toxicity to represent adverse selection risk in the HFT context. In the authors words order flow is regarded as toxic when it adversely selects market makers who may be unaware that they are providing liquidity at a loss (p. 1458). Thus, in this case, adverse selection must be understood not only as a problem of asymmetric information but also as a wider notion that may encompass other risks related to liquidity provision. When order flows are essentially balanced, high frequency market makers have the potential to earn razor thin margins on massive numbers of trades. When order flows become unbalanced, however, market makers face the prospect of losses due to adverse selection. These market makers estimates of the time-varying toxicity level now becomes a crucial factor in determining their participation. If they believe that toxicity is high, they will liquidate their positions and leave the market. To measure order flow toxicity Easley et al. (2012a) present the Volume Synchronized Probability of Informed Trading or VPIN metric, a new procedure to estimate the probability of informed trading based on volume imbalance and trade intensity. VPIN is inspired by the well-known PIN model of Easley et al. (1996), henceforth EKOP (1996). The PIN is a consolidated model to measure the presence of informed traders that has been widely adopted to address a variety of issues in the empirical financial literature, among others: information content of the time between trades (Easley et al., 1997a), trade size (Easley et al., 1997b), analyst coverage (Easley et al., 1998), electronic market order flow (Brown et al., 1999), stock splits (Easley et al., 2001), dealer vs. auction markets (Heidle and Huang, 2002), asset pricing (Easley et al., 2002; Aslan et al., 2011), non-anonymous vs. anonymous trading systems (Gramming et al., 2001), market reaction to public and private information (Vega, 2006), corporate investment decision (Ascioglu et al., 2008; Chen et al., 2007), block ownership (Brockman and Yan, 2009), and market anomalies (Kang, 2010; Chen and Zhao, 2012). However, the PIN is not extent from criticism. First, there is a growing debate as to the appropriateness of PIN in measuring information-based trading (Aktas et al., 2007; Duarte and Young, 2009; Easley et al., 2010; Akay et al., 2012). Second, several papers show that the PIN estimations could suffer several biases for different reasons such as trade misclassification (Boehmer et al., 2007), boundary solutions or the floating-point exception, especially in very active stocks (Easley et al., 2010; Lin and Ke, 2011; Yan and Zhang, 2012), and propose different solutions to mitigate such biases. PIN and VPIN models require trading volume classified as buy or sell and are based on the notion that order imbalances signal the presence of adverse selection risk. However, the VPIN approach has some practical advantages over the PIN methodology that make it particularly attractive for both practitioners and researchers. The main advantage is that VPIN does not require the estimation of nonobservable parameters using optimization or numerical methods thereby avoiding all the associated computational problems and biases. In addition, VPIN allows the capturing of risk variations at intraday level while the original PIN model does not. In a series of related papers Easley et al. (2011a, 2011b, 2012a) present the VPIN as a useful tool for different market participants. Easley et al. (2011a) show the VPIN of the e-mini S&P500 futures contract achieving its maximum level around the Flash Crash. Higher levels of toxicity force HF market makers to liquidate their positions and leave the market offering a plausible explanation of the Flash Crash. The authors recommend that regulators use VPIN as a warning tool that could herald the implementation of regulatory actions to forestall crashes. 3 Easley et al. (2012a) also show that VPIN has forecasting power over volatility (toxicityinduced) and could become valuable as a risk management tool for market making activity. It can be also useful for trading strategies based on volatility arbitrage and for brokers who look for best time of execution. Easley et al. (2011b) present the specifications of a VPIN contract, which could be used to hedge against the risk of higher than expected levels of toxicity as well as to monitor such risk. On the other hand, Andersen and Bondarenko (2011) put forward several criticisms questioning the predictive power of VPIN. In particular, the authors document that VPIN is a poor predictor of short run volatility with a limited predictive power emanating from the mechanical relation to the underlying trading intensity. Andersen and Bondarenko s analysis provoked a speedy response from Easley et al. (2012d) who basically point to the confusion in the methodology they use, the analysis they perform and the conclusions they draw. Using a selected sample of 15 Spanish stocks, the main objective of this paper is to offer a detailed description of the VPIN estimation procedure, its key variables, and its usefulness in an attempt to gain a better understanding of this novel tool. Departing from the PIN model, we document the main innovations introduced in this updated version of the probability of informed trading and we analyze the compatibility of both models. To the best of our knowledge, this is the first study to apply VPIN methodology to a sample of European stocks. 4 Although the relevance of HFT in the Spanish Stock Exchange has not yet been formally measured, mostly because of data availability problems, informal conversations with regulators corroborate the interest of HF traders in the most active stocks listed on the Spanish market. Our results suggest that certain VPIN specifications provide proxies for adverse selection risk similar to those obtained by the PIN model. In this sense, we consider that the key variable in the VPIN procedure is the number of buckets used, so estimations of VPIN using one bucket are quite similar to those obtained by the PIN model. We conclude that VPIN is, in the main, a straightforward way to measure adverse selection but not exclusively for the high frequency environment. The paper is organized as follows: Section 2 briefly reviews the PIN model. Section 3 focuses on VPIN putting special emphasis on the main innovations it incorporates and its computational procedure. Section 4 describes the Spanish stock market and the sample employed. Section 5 compares PIN to VPIN aggregated values. Section 6 concludes. 2. PIN model (EKOP 1996) The probability of information-based trading (PIN) is a measure of the information asymmetry between informed and uninformed trades that builds on the theoretical work of Easley and O Hara (1987, 1992). The original PIN model was introduced by Easley et al. (1996). Since then, various empirical papers have implemented, adapted, and improved the PIN approach (Easley et al., 1997a,b, 1998, 2008). The PIN measure is not directly observable but is a function of the theoretical parameters of a microstructure model that have to be estimated by numerical maximization of a likelihood function. The model views trading as a game between liquidity providers and traders (position takers) that is repeated over trading days. 3 Bethel et al. (2012) confirm that VPIN could have given a strong signal ahead of the Flash Crash event on May 2010 and it can be use for a fully-fledged early warning system for unusual market conditions. 4 Up to now, VPIN has been mainly applied to high-frequency trading futures contracts.

3 D. Abad, J. Yagüe / The Spanish Review of Financial Economics xxx (2012) xxx xxx 3 Trades can come from informed or uninformed traders. For any given trading day the arrival of buy and sell orders from uniformed traders, who are not aware of the new information, is modeled as two independent Poisson processes with daily arrival rates ε b and ε S, respectively. The model assumes that information events occur between trading days with probability. Informed traders only trade on days with information events, buying if they have seen good news (with probability 1 ı) and selling if they have seen bad news (with probability ı). The orders from the informed traders follow a Poisson process with daily arrival rate. 5 Under this model, the likelihood of observing B buys and S sells on a single trading day is: PIN EKOP, 1996 Fundamental Information Clock-time Itemized classification VPIN Easley et al., 2012a Broader definition of Information Volume-time Bulk classification L((B, S) ) = (1 )e ε (ε b b) B (ε s) S B! e εs S! + ıe ε (ε b b) B (ε B! e (εs+) s + ) S S! + (1 ı)e (ε b +) (ε b + ) B e (ε s) S εs (1) B! S! where B and S represent total buy trades and sell trades for the day, respectively, and = (, ı,, ε b, ε s ) is the parameter vector. This likelihood function is a mixture of three Poisson probabilities, weighted by the probability of having a good news day (1 ı), a bad news day ı, and no-news day (1 ). Assuming crosstrading day independence, the likelihood function across J days is just the product of the daily likelihood functions: L(M ) = J L( B j, S j ) (2) j=1 where B j, and S j are the numbers of buy and sell trades for day j = 1,..., J, and M = [(B 1, S 1 ),..., (B J, S J )] is the data set. Maximization of (2) over given the data M yields maximum likelihood estimates for the underlying structural parameters of the model (, ı,, ε b, ε s ). Once the parameters of interest are estimated, the Probability of Informed Trading, PIN, is calculated as: PIN = (3) + ε b + ε s where + ε b + ε s is the arrival rate of all orders, is the arrival rate of informed orders. The PIN is thus the ratio of orders from informed traders to the total number of orders. An attractive feature of the EKOP methodology is its apparently modest data requirement. All that is necessary to estimate the model is the number of buy- and sell-initiated trades for each stock and each trading day. However a shortcoming of the EKOP methodology is that, although the estimation procedure is straightforward, it often encounters numerical problems when performing the estimation in practice. Especially in stocks with a huge number of trades, the optimization program may bump into computational overflow or underflow (floating-point exception) and as a consequence it may not be able to obtain an optimal solution. Several numerical methods have been used for solving the maximization problem; for instance, Easley et al. (2010) and Lin and Ke (2011) propose two different factorizations of the likelihood function to facilitate numerical maximization. However, the convergence of optimization algorithm is not always possible and the method fails to deliver the PIN to certain active stocks. These difficulties in estimating PIN have worsened in the last year due to the steady increase in the number of trades which are a consequence, among other reasons, of the growth in automated trading and structural 5 A more extensive discussion of this structure can be found in EKOP (1996). No-explicit role for trade intensity Trade intensity matters Fig. 1. VPIN innovations. Figure outlines the four main innovations that Easley et al. (2012a) introduce in the VPIN model dealing with the PIN original model developed by EKOP (1996). changes in the market that have greatly reduced market depth (Aslan et al., 2011). 3. VPIN model (Easley et al., 2012a) The fundamental link between PIN and VPIN can be found in Easley et al. (2008). Departing from EKOP (1996) PIN model as a benchmark, these authors develop a dynamic econometric model of trading by introducing time-varying (GARCH-style) arrival rates of informed and uninformed traders. They show that for a particular period of time (e.g., days), the expected trade imbalance E[V Sell V Buy ] approximates (PIN numerator) while the expected total number of trades E[V Sell + V Buy ] equals + ε b + ε s (PIN denominator). Before detailing the VPIN approach, Fig. 1 outlines the main innovations that Easley et al. (2012a) introduce regarding the original PIN model. The first two innovations basically make reference to the update of the model to the high frequency environment. The first one is the broader definition of information that underlies VPIN. The PIN model focuses on fundamental information about the true value of the stock. In the PIN model, information about stock value arrives with a certain probability on a particular day. Then, informed traders emerge on the right side of the market unbalancing trading activity. VPIN measures order flow toxicity and toxicity is a wider concept focusing on the likelihood of HF liquidity providers being adversely selected. Adverse selection may include fundamental information but also other factors related to the nature of the trading in the overall market or to the specifics of liquidity demand over a particular interval. Therefore, information in VPIN is related to underlying events that provoke unbalanced or accelerated trade over a relatively short horizon including not only those related to asset returns, but also others reflecting more systemic or portfolio-based effects. The second divergence is the different time system on which both models work. The PIN model works on clock-time while VPIN works on volume-time. The PIN model collects daily order imbalances under the assumptions of daily independence and price efficiency at the end of the day. In contrast, VPIN computes order imbalance on every occasion the market exchanges a constant amount of volume (volume bucket) mimicking the arrival to the market of news of comparable relevance. Sampling by volume is equivalent to dividing the trading session into periods of

4 4 D. Abad, J. Yagüe / The Spanish Review of Financial Economics xxx (2012) xxx xxx Table 1 VPIN metric procedure sample excerpt. Time Price Volume Time Price Volume Time Price Volume 09:06: :08: :07: ,000 09:08: :05: :07: :08: :06: :07: :09: :06: :07: :09: :06: :07: :09: :06: :07: :09: :06: :07: :09: :06: :07: :09: :06: :07: :09: :06: :07: :10: :06: :07: :10: :06: :08: :10: :06: :08: :11: :06: :08: :11: :06: :08: :11: :06: :08: :11: ,600 09:06: :08: :11: :06: :08: :11: :06: ,882 09:08: :12: :06: :08: :06: :08: Table presents a small excerpt of the transaction data (time, price and volume) necessary to calculate VPIN. The data corresponds to several minutes on the first trading day of the year 2009 for a high frequently traded stock in the Spanish market (Telefónica, TEF). comparable information content reducing, in this way, the impact of volatility clustering in the sample. 6 The third innovation supposes an incidental contribution (Easley et al., 2012a, p. 1459) that is beyond even the VPIN computation. In particular, the PIN model employs an itemized classification to distinguish between buy and sell volume while VPIN proposes a new approach labeled bulk classification. In the PIN model order imbalance is observed by signing tick-by-tick trades. The Lee Ready algorithm is commonly used for this task in those markets where it is not possible to distinguish the aggressor s side of the trade. In VPIN, Easley et al. (2012a) argue that, particularly in high frequency settings, itemized approaches are problematic even if classification algorithms are not necessary at all. These authors propose to compute order imbalances by aggregating trades over short time intervals (time bars) or volume intervals (volume bars) and then using normal distribution and standardized price changes to determine the percentage of buy and sell volume. Nevertheless, VPIN computation is also possible using an itemized approach for raw data. 7 Finally, in the original PIN model, order imbalances are observed in terms of number of buys and sells, regardless of the trade size. 8 In contrast, VPIN takes into account trade size by treating each reported trade as if it were an aggregation of trades of unit size. This convention explicitly puts trade intensity into the analysis. It is also important to mention that the output and estimation procedure of the models also differ. The PIN model provides a single estimation of the probability of informed trading for a particular period of time (year, month) that is obtained once non-observable parameters are estimated by maximum likelihood. VPIN procedure produces a serial of estimations of the VPIN metric for a time period 6 Easley et al. (2012c) argue that the defining characteristic of HFT is not the speed but the presence of strategic traders operating in volume-time or eventbased time. 7 Easley et al. (2012b) examine in detail this bulk classification for any microstructural application where the classification of the aggressor s side of a trade could be necessary. They conclude that working with tick data for inferring buy and sell volume is not only inefficient and costly, but also does not offer greater accuracy compared to time or volume bars. 8 Easley et al. (1997b) introduce trade size in PIN estimation but only in terms of large or small buys and sells. and does not require intermediate estimation of non-observable parameters or the application of numerical methods. This serial measure also allows the capture of risk variations at intraday levels but taking into account that an individual VPIN observation is not relevant itself but only in reference to their empirical distribution. In this paper our main goal is to analyze PIN and VPIN compatibility so we focus more on aggregate VPIN metrics (average, median, standard deviation) than on particular values of this measure VPIN metric procedure To illustrate VPIN estimation procedure we opt for using an example rather than repeat the specific formulation and the algorithm that are available in Easley et al. (2012a). We depart from a tick-to-tick sample of transactions of a particular instrument with the following information: time of the trade, price and volume exchanged. Table 1 shows a small excerpt of transaction data for one high frequently traded stock of the Spanish market, Telefónica (ticker TEF ), on date 02/01/ Time (or volume) bars The original procedure begins with trade aggregation in time (or volume) bars. Although this first step is not enforced and it is possible to work with raw transaction data, Easley et al. (2012a) assert that data aggregation leads to a better identification of buy and sell volume and thus, better flow toxicity estimates. Bar size is the first key variable of the VPIN computation process. Following Easley et al. (2012a) we use a 1-min time bar. In each time bar, trades are aggregated by adding the volume of all the trades in the bar (if any) and by computing price change for this period of time. 9 After that and in order to take into account trade size, the sample is expanded by repeating each bar price change as many times as the volume in the bar. Thus, the original raw sample became a 9 Volume bars operates analogously. In this case, bar size is defined in terms of a fixed number of shares (or contracts) instead of a particular period of time. Easley et al. (2012a) argue that time bars are a more familiar concept to market practitioners since several data vendors (e.g., Bloomberg) commonly provide aggregated data for particular periods of time.

5 D. Abad, J. Yagüe / The Spanish Review of Financial Economics xxx (2012) xxx xxx 5 Table 2 VPIN metric procedure time bars. Time bar (TB) TB price change ( P) TB volume 9:05:01 9:06:00 9:06:01 9:07: = ,542 9:07:01 9:08: = ,726 9:08:01 9:09: = ,996 9:09:01 9:10: = :10:01 9:11: = :11:01 9:12: = 0 46,797 9:12:01 9:13:00 Table shows time bar completion in our example. Time Bar (TB) presents the 1- min time bars that can be computed from the example excerpt. TB Price Change ( P) reflects the price change that takes place in each bar. Finally, TB Volume is the aggregated volume of all trades that take place into the minute. This volume has the interpretation of the number of one-unit independent trades. sample of one-unit trades each of them associated with the price change of the corresponding bar. Table 2 shows Time Bar (TB) computation in our example. We can calculate six 1-min bars (from 9:07 to 9:12) from the small sample excerpt in our example. TB Volume is the accumulated volume of all transactions that take place in the corresponding minute and TB Price Change ( P) represents the variation of transaction price from the last price in the corresponding time bar to the last available in the previous one. The sample is then expanded by considering trades of one unit that are associated with the corresponding price change. For example, in time bar 9:07 instead of considering that we have a unique transaction of 44,542 shares we consider 44,542 (independent) one-unit trades, each of them associated with a price change of Volume buckets and bulk classification Volume bucket (or volume bin) is the second essential variable in VPIN metric. Volume buckets represent pieces of homogeneous information content that are used to compute order imbalances. In Easley et al. (2012a) volume bucket size (VBS) is calculated by dividing the average daily volume (in shares) by 50 which is the number of buckets they initially consider. Therefore, if we depart from the average daily volume, it is the number of buckets which fully determines VBS. Consequently, we consider the number of buckets as our second key variable. Buckets are filled by adding the volume in consecutive time bars until completing the VBS. If the volume of the last time bar needed to complete a bucket is for a size greater than required, the excess size is given to the next bucket. In general, a volume bucket needs a certain number of time bars to be completed although it is also possible that the volume in a time bar could be enough to fill one (or more) volume buckets. Table 3 shows the bucket assignation process. The average daily volume for TEF in 2009 was 21,158,426 shares. Following Easley et al. (2012a) we use 50 buckets and obtain a VBS of 423,168 shares. Bucket #1 starts to fill from the first time bar. When the volume of the 9:06 time bar is included, bucket #1 accounts for 380,695 shares and 42,423 shares are pending to complete it. The following time bar is 9:07 with an associated volume of 44,542 shares, 42,423 of which are used to complete bucket #1 and the remaining 2069 shares are assigned to the following bucket (bucket #2). Bucket #2 is completed in the 9:20 time bar. At the same time of bucket completion, time bar volume is classified as buyer- or seller-initiated in probabilistic terms. Normal distribution is employed labeling as buy the volume that results from multiplying the volume bar by the value of the normal distribution evaluated in the standardized price change Z( P/ P ). To standardize, we divide the corresponding price change by the standard deviation of all price changes for the whole sample. Analogously, we categorize as sell the volume that results from multiplying the volume bar by the complementary of the normal distribution for the buy side, 1 Z( P/ P ). In the last columns of Table 3, we observe buy and sell distribution of volume bars in our example. The standard deviation of all price changes for our sample is For time bars with a null price change, the probabilistic method allocates one half of the volume as buy and one half as sell. The volume of the time bars with positive price changes are mainly classified as buy while the volume of the time bars with negative price changes are mainly classified as sell. The higher the price change in absolute terms the higher the asymmetry of the classified volume Order imbalance Order imbalance (OI) is computed for each bucket by simply obtaining the absolute value of the difference between buy volume and sell volume in the assigned time bars. 10 Table 4 shows order imbalance for the first ten buckets. It is important to point out that some buckets need short clock-time to be completed (e.g., bucket #1) while others need longer periods of time (e.g., bucket #10) VPIN and sample length In the last step we finally obtain VPIN values. To do that, it is necessary to define a new variable: sample length (n). This variable establishes the number of the buckets with which VPIN is computed. Following the link established in Easley et al. (2008). E[V Sell V Buy ] VPIN = + ε b + ε s E[V Sell + V Buy = ] n =1 OI n VBS where VPIN is simply the average of order imbalances in the sample length, that is, the result of dividing the sum of order imbalances for all the buckets in the sample length (proxy of the expected trade imbalance) by the product of volume bucket size (VBS) multiplied by the sample length (n) (proxy for the expected total number of trades). VPIN metric is updated after each volume bucket in a rolling-window process. For example, if the sample length is 50, when bucket #51 is filled, we drop bucket #1 and we calculate the new VPIN based on buckets #2 to #51. Easley et al. (2012a) firstly consider sample length equal to the number of buckets (50), but throughout the paper the authors change this variable to 350 or 250 depending on what they want to analyze. A sample length of 50 buckets when the number of buckets is also 50 is equivalent to obtaining a daily VPIN. A sample length of 250 (350) when the number of buckets is 50 is equivalent to obtaining a five-day (seven-day) VPIN. Table 5 shows the first ten VPIN values for TEF in the year 2009 using a sample length of 50 buckets (n = 50). As 50 buckets are necessary to obtain VPIN, our first value of VPIN is obtained once bucket #50 is filled. Finally, Fig. 2 shows the complete VPIN series for TEF in the year 2009 using 1-min time bars, 50 buckets to compute the VBS and 50 buckets as sample length. Table 6 reports basic statistics of this series. To summarize the VPIN estimation procedure, we briefly review the three levels in which the VPIN calculation takes place: (1) buy and sell classification occurs at bar level (time or volume) where bar size is the key variable. At this level, individual trades are aggregated and the resulting volume is then classified as buyer- or seller-initiated using a probabilistic method based on 10 Andersen and Bondarenko (2011) experiment with signed order imbalances instead of absolute ones concluding that signed imbalances may contain useful information for gauging real-time market stress indicators. (4)

6 6 D. Abad, J. Yagüe / The Spanish Review of Financial Economics xxx (2012) xxx xxx Table 3 VPIN metric procedure volume bucketing and bulk classification. Time bar (TB) TB price change ( P) TB volume Accumulated volume bucket #Bucket Z( P/ P ) 1 Z( P/ P ) Buy volume Sell volume 9:00:01 9:01: ,405 91,405 # , :01:01 9:02: , ,120 # ,715.0 #1 9:05:01 9:06: , ,695 #1 9:06:01 9:07: , ,168 # , :06:01 9:07: # :07:01 9:08: ,726 22,795 # , :08:01 9:09: ,996 44,791 # , :09:01 9:10: ,828 # :10:01 9:11: ,617 # :11:01 9:12: ,797 99,414 #2 9:12:01 9:13:00 #2 #2 9:19:01 9:20: , ,168 # , :19:01 9:20: ,486 20,486 # ,476.0 Columns 1 5 describe the bucket assignation process. Buckets are filled by adding the volume in consecutive time bars until reaching 423,168 shares which is the volume bucket size (VBS). If the volume of the last time bar needed to complete a bucket is for a size greater than required, the excess size is given to the next bucket. Bold rows indicate the time bar when a bucket is completed. Columns 6 9 display the probabilistic method to classify buyer- and seller-initiated volume for each time bar. Columns 6 and 7 present the value of normal distribution evaluated in the standardized price change ( P/ P ) and the complementary, respectively. Columns 8 and 9 are the result of multiplying TB Volume (column 4) by the value in columns 6 and 7, respectively. Table 4 VPIN metric procedure order imbalance. #Bucket Aggregated buy volume Aggregated sell volume Order imbalance Initial time bar Final time bar #1 134, , , :01:00 09:07:00 #2 261, , , :07:00 09:20:00 #3 234, , , :20:00 09:31:00 #4 140, , , :31:00 09:46:00 #5 261, , , :46:00 10:01:00 #6 263, , , :01:00 10:16:00 #7 285, , , :16:00 10:31:00 #8 188, , , :31:00 10:49:00 #9 285, , , :49:00 11:00:00 #10 176, , , :00:00 11:29:00 #11 Table presents order imbalances for the first ten buckets for TEF in the year Aggregated Buy (Sell) Volume is the sum of all buy-initiated (sell-initiated) volume of the corresponding time bars for each bucket. The sum of both columns in each row equals the VBS. Order Imbalance is the difference between values in columns 2 and 3. Finally, the lasts two columns indicate the initial and the final time bar of the corresponding bucket, respectively. normal distribution and standardized price change. This level is what Easley et al. (2012a) denominate Bulk classification. Regarding bar size, the authors show that within reasonable bounds the Table 5 VPIN metric procedure VPIN and sample length. Obs VPIN Initial #bucket Final #bucket #1 # #2 # #3 # #4 # #5 # #6 # #7 # #8 # #9 # #10 #59 Table presents the first ten values of VPIN for TEF in the year VPIN is computed using 1-min time bars, 50 volume buckets and a sample length (n) of 50 buckets. VPIN is the ratio between the expected trade imbalance (approximated by the sum of the bucket order imbalances in the sample length) and the expected total number of trades (approximated by volume bucket size, VBS, multiplied by the sample n E[V Sell length), VPIN = +ε = OI =1 b +εs E[V Sell ] n VBS VPIN metric is updated after each bucket completion in a rolling-window process. Thus, when bucket 51 is filled, we drop bucket #1 and calculate a new VPIN observation focus on buckets #2 to #51. V Buy ] +V Buy choice of the amount of time contained in a time bar has little effect in measuring order imbalances. (2) Order imbalance is computed in absolute terms at bucket level where the number of buckets is the key variable. Working in volume-time provides VPIN /09 02/09 04/09 05/09 07/09 10/09 12/09 Date TEF VPIN Fig. 2. Telefónica (TEF) VPIN Figure shows VPIN series for TEF in the year 2009 using 1-min time bars, 50 buckets to compute the VBS and 50 buckets as sample length (TEF VPIN ).

7 D. Abad, J. Yagüe / The Spanish Review of Financial Economics xxx (2012) xxx xxx 7 Table 6 TEF VPIN 2009 statistics. Statistics VPIN Average Median Std. deviation Max Min # Obs. 12,650 Table reports basic statistics for VPIN series of TEF stock in the year 2009 using 1- min time bars, 50 buckets to compute the VBS and 50 buckets as sample length (TEF VPIN ). a more accurate scenario with which to accomplish HFT strategies (Easley et al., 2012b) with volume buckets representing units of homogeneous information. In our opinion, this is the more relevant variable of VPIN metric procedure. In principle, there is no formal justification in Easley et al. (2012a) for choosing 50 buckets or any other specific quantity. It seems clear that when the number of buckets is high enough, resulting order imbalances may be capturing the different components of the adverse selection risk faced by HF liquidity providers. However, it seems unclear what kind of toxicity is measured when a lower number of buckets is employed. For example, if we opt to work with one bucket, by definition, we are computing a daily order imbalance on average which is quite similar to the PIN model where order imbalances are computed on a daily basis. Therefore, it is possible that the information content (and thus, the nature of toxicity) differs from a VPIN computed using one bucket to another VPIN computed using a higher number of buckets. (3) Finally, VPIN values are approximated by the average of a particular number of bucket order imbalances in a rolling-window process. Sample length is the key variable in this level and, once again, there is no formal discussion for using a particular value for this variable. 4. Market description, data, and sample Our sample is made up of stocks traded on the electronic trading platform of the Spanish Stock Exchange, known as the SIBE (Sistema de Interconexión Bursátil Español). The SIBE is an order-driven market where liquidity is provided by an open limit order book. Trading is continuous from 9:00 am to 5:30 pm. There are two regular call auctions each day: the first one determines the opening price (8:30-9:00 am), whereas the second one sets the official closing price (5:30-5:35 pm). A continuous session could be interrupted by a system of stock-specific intraday price limits and short-lived call auctions directed to handle unusual volatility levels. In all auctions (open, close and volatility) orders can be submitted, modified or canceled, but no trades occur. Three basic types of orders are allowed: limit orders, market orders, and market-to-limit orders. In the continuous session, a trade occurs whenever an incoming order matches one or more orders on the opposite side of the limit order book. Orders submitted that are not instantaneously executed are stored in the book waiting for a counterparty according to a pricetime priority rule. Unexecuted orders can always be canceled and modified. Trade and quote data for this study come from SM data files provided by Sociedad de Bolsas, S.A. SM files comprise detailed timestamped information about the first level of the limit order book for each stock listed on the SIBE. Any trade, order submission or cancelation that affects best prices in the book generates a new record. The distinction between buyer-initiated and seller-initiated trades is straightforward, without the need to use any classification algorithm. Our sample comprises 15 Spanish stocks for the year 2009 split into three 5-stock portfolios typifying different levels of capitalization, activity and liquidity (large, medium and small). To do that, the five stocks of each portfolio were chosen at random from those belonging the entire year to the IBEX-35 index, the IBEX MEDIUM CAP index, and the IBEX SMALL CAP index, respectively. The IBEX-35 index comprises the biggest, most liquid and frequently traded stocks in the SIBE, whereas the stocks in the other two indexes are smaller, less frequently traded and more illiquid. 11 In Table 7, we provide sample statistics on several commonlyused market indicators of trading activity, volatility and liquidity. As expected, market capitalization, trading activity and liquidity decreases as we move from the large portfolio to the small one. Overall, we observe that stocks in the large portfolio are on an average much more traded and liquid than the stocks belonged to the other two groups. In any case, we test the equality of the different market indicators between the three portfolios (Kruskal-Wallis test) and between each pair (Mann-Whitney test). All the tests performed are rejected at 5% significance level with the exception of those related with the volatility proxy (not reported but available upon request). 5. Empirical evidence: PIN and VPIN comparison In this section we compare the VPIN model with its predecessor PIN by applying both methods to the same stock sample. As we have discussed, both models are based on the observation of order imbalances to measure the probability of being adversely selected. VPIN is introduced as the updated version of PIN in a double sense: (1) as a new tool designed to deal with the new risks from the new market paradigm of HFT, and (2) as a straightforward approach to obtain the probability of being adversely selected while avoiding the most important drawbacks of the PIN model. In the previous section, we have reviewed VPIN procedure paying special attention to the main innovations introduced and the key variables for its computation. By comparing PIN and VPIN in this section our main goal is to stress the role of VPIN as an easy way to measure adverse selection (or order flow toxicity) not only to the HFT environment. We estimate first the PIN model via maximum likelihood for each stock and month in Easley et al. (1997a) indicate that a 30 trading-day window allows sufficient trade observations for the PIN estimation procedure. Akay et al. (2012) use 20 trading days to estimate PIN finding numerical solutions for all their estimations. Hence, the use of one-month transaction data (around 20 trading days) should be wide enough to produce reliable estimates. We use the optimization algorithm of the Matlab software to maximize the likelihood function in (2). We usually run the maximum likelihood function 100 times for each stock-month pair in our sample, except for several months of large stocks for which we increase the iterations to 1000 to ensure that a maximum is reached. We follow Yan and Zhang (2012) to set initial values for the five parameters in the likelihood function. The estimation procedure converges for virtually all the 60 stock-month combinations of our sample. 11 The IBEX35 index is made up of the 35 most liquid stocks traded on the SIBE and is the benchmark stock market index. The IBEX MEDIUM CAP index and the IBEX SMALL CAP index are representative of the medium and small capitalization companies traded on SIBE, respectively. In order to be eligible for the IBEX MEDIUM CAP and IBEX SMALL CAP, the stocks shall not be included in the IBEX 35, they must be listed in the main trading market, have a free float above 15% and an annualized rotation of at least 15% of their real free float capitalization. The stocks that meet the previous criteria will be ranked by free float capitalization. The first 20 companies of the ranking will be the constituents of the IBEX MEDIUM CAP index and the next 30 will form the IBEX SMALL CAP index. All the indexes are price-style weighted by capitalization and adjusted according to the free float of each company. The Technical Advisory Committee of the IBEX indices selects the constituents of these indexes in two ordinary meeting per year (June and December), although extraordinary meetings are also possible due to special circumstances. The reader can find information about theses stock indexes in:

8 8 D. Abad, J. Yagüe / The Spanish Review of Financial Economics xxx (2012) xxx xxx Table 7 Sample statistics. Company name Ticker Capitalization (D millions) Frequency Volume (D millions) Volatility Relative Spread Depth (D thousands) Amihud Iliq. ( 10 9 ) Panel A: Large Banco Bilbao Vizcaya BBVA 47, Iberdrola IBE 35, Inditex ITX 27, Banco Popular POP Telefónica TEF 89, Average 41, Panel B: Medium Corporación Alba ALB Ebro Puleva EVA Catalana Occidente GCO Banco Pastor PAS Zardoya Otis ZOT Average Panel C: Small Amper AMP Barón de Ley BDL Campofrio CFG Europac PAC Service point solutions SPS Average Table presents the 15 stocks included in the sample grouped in three 5-stock portfolios: Large (stocks from IBEX35 index in Panel A), Medium (stocks from IBEX MEDIUM CAP index in Panel B), and Small (stocks from IBEX SMALL CAP index in Panel C). For each stock, the table reports the market capitalization at the end of 2009 and the mean of different daily indicators of trading activity, volatility, and liquidity. Activity proxies are the number of trades (frequency) and the traded volume in millions of Euros. Volatility proxy is the high-low quote midpoint ratio. Liquidity measures are the relative spread and market depth (bid + ask) in thousands of Euros. Both liquidity measures are daily mean weighted by time. Amihud Iliq. is the measure of illiquidity proposed by Amihud (2002) which consists of the mean of the daily ratio between return and traded volume. Summary statistics for PIN parameters and PIN values are reported in Table 8. First, we compute mean values across months for each stock and then, we report the cross-sectional mean, median and standard deviation for each portfolio. As expected, we find that the probability of informed trading increases as we move to lower levels of trading activity and liquidity. The mean (median) results show that PIN is (0.098) for large portfolio, rising to (0.158) for medium, and it reaches (0.247) for the stocks included in the small portfolio. These results are consistent with EKOP (1996) findings, and also with those of Abad and Rubia (2005) who also analyze the PIN model for the Spanish stock market. The analysis of PIN parameters can provide more information about the origin of the observed differences in PIN values among portfolios. According to Eq. (3), PIN is positively related to the probability of an information event ( ) and negatively related to the ratio of the arrival rate of uninformed trades to the arrival rate of informed trades ((ε b + ε s )/). From Table 8 we can observe similar value in the three portfolios. Using Kruskal Wallis and Mann-Whitney tests (not reported) we reject that this probability statistically differs among the three groups. On the contrary, we can observe how the uninformed-to-informed ratio dramatically decreases as we move from the most active to the less frequently traded stocks (using mean values, from 2.60 for large stocks to 1.32 for medium, being 0.74 for small stocks). Hence, our results suggest that asymmetric information risk is higher for the more illiquid and less frequently traded stocks due to the fact that proportionally there are fewer Table 8 PIN and VPIN statistics. Large Medium Small Mean Median Std. dev Mean Median Std. dev Mean Median Std. dev ı ε b ε s PIN VPIN VPIN VPIN VPIN VPIN VPIN VPIN VPIN Table presents the cross-sectional statistics of the estimated parameters of the PIN model, PIN values and eight VPIN series using different specifications of the key variables. The parameter represents the probability that an information event will occur on a particular day, ı is the probability that an information event will be negative, ε b and ε s are the arrival rates of uninformed buyers and sellers, respectively, and represents the arrival rate of informed traders on information days. PIN is the probability of informed trade. The three digits that appear beside the acronym VPIN make reference to time bar size (min), number of buckets and sample length, respectively.